What is meant by a circle's diameter?

Complete question is;

The cost of producing x units of a particular commodity is C(x) = ⅔x² + 6x + 45 shillings and the production level t hours into a particular production run is x(t) = 0.3t² + 0.04t. At what rate is cost changing with respect to time after 5 hours?

Answer:

dC/dt = 49.45

Step-by-step explanation:

Since C(x) = ⅔x² + 6x + 45

And x(t) = 0.3t² + 0.04t

This means that;

C(x) = C(x(t))

The rate at what cost is changing with respect to time is given as;

dC/dt

Thus, from chain rule;

dC/dt = (dC/dx) × (dx/dt)

dC/dx = (4/3)x + 6

dx/dt = 0.6t + 0.04

Now, when t = 5, then;

x(5) = 0.3(5)² + 0.04(5)

x = 7.7

Thus;

dC/dx = (4/3)x + 6 = (4/3)(7.7) + 6 = 16.267

At 5 hours,

dx/dt = 0.6(5) + 0.04 = 3.04

Thus;

dC/dt = 16.267 × 3.04

dC/dt = 49.45

We have a function,

[tex]f(x)=x^2-1[/tex]

and we are asked to find its inverse function.

An inverse function essentially gets you the original value that was dropped into a function.

For example,

If I put 5 into [tex]f(x)[/tex] I will get 24. Now If I take 24 and put it into the inverse function I have to get number 5 back.

The way to determine the inverse function swap the x and the [tex]f(x)[/tex], then solve for [tex]f(x)[/tex],

[tex]x=f(x)^2-1[/tex]

[tex]f(x)^2=x+1[/tex]

[tex]f(x)=\pm\sqrt{x+1}[/tex]

Of course the notation demands that the obtained function be called,

[tex]f^{-1}(x)=\pm\sqrt{x+1}[/tex]

Hope this helps :)

Answer:

Hence the answer is TRUE.

Step-by-step explanation:

If event A is taking 15 or more minutes to urge to figure tomorrow and event B is taking but a quarter-hour to urge to figure tomorrow, then events A and B must be complimentary events. this is often because the occurring of 1 is going to be precisely the opposite of the occurring of the opposite event and that they cannot occur simultaneously. In other words, events A and B are mutually exclusive and exhaustive.  

Mathematically,  

P(A) + P(B) = 1.

Answer:

6x + 10y

Step-by-step explanation:

4x + 3y + 2x + 7y

=> (4x + 2x) + (3y + 7y)

=> 6x + 10y

Step-by-step explanation:

Fractions represent equal parts of a whole or a collection. 

Fraction of a whole: When we divide a whole into equal parts, each part is a fraction of the whole. 

a fraction has 2 parts

The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken.  The number below the line is called the denominator.  It shows the total divisible number of equal parts the whole into or the total number of equal parts which are there in a collection. 

There are different types of fraction

Answer:

(-5, 0) and (5, 0)

Step-by-step explanation:

This equation fits the form for a hyperbola with x-intercepts.  The standard form for such an equation is

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]

To get the equation in the question into this standard form, divide each term by 400.

[tex]\frac{16x^2}{400}-\frac{25y^2}{400}=\frac{400}{400}\\\frac{x^2}{25}-\frac{y^2}{16}=1[/tex]

To find the x-intercepts, make y = 0.

[tex]\frac{x^2}{25}=1\\x^2=25\\x=\pm 5[/tex]

The vertices are located at the points (-5, 0) and (5, 0).

Note: There are no y-intercepts; making x = 0 produces no real solutions for y.

Answer:

They walked a total distance of 290 miles every morning.

Step-by-step explanation:

First, we have to subtract 214 and 138.

= Jay walks 76 miles.

Next, we have add 214 and 76.

= 290 mi.

Answer:

The correct answer is the letter C.

Step-by-step explanation:

We can use the following trigonometric identity:

[tex]cos(60)=\frac{6}{b}[/tex] (1)

[tex]cos(45)=\frac{c}{b}[/tex] (2)

Solving each equation by b and equaling we have:

[tex]\frac{6}{cos(60)}=\frac{c}{cos(45)}[/tex]

[tex]\frac{6}{cos(60)}=\frac{c}{cos(45)}[/tex]

Let's recall that:

[tex]cos(45)=\frac{1}{\sqrt{2}}[/tex]

[tex]cos(60)=\frac{1}{2}[/tex]

Then we have:

[tex]c=\frac{cos(45)*6}{cos(60)}[/tex]

[tex]c=\frac{2*6}{\sqrt{2}}[/tex]

[tex]c=\frac{12}{\sqrt{2}}[/tex]

[tex]c=6\sqrt{2}[/tex]

Using equation (1) we can find b.

[tex]cos(60)=\frac{6}{b}[/tex]  

[tex]b=12[/tex]      

Finally, we can find a using the next equation:

[tex]tan(60)=\frac{a}{6}[/tex]

[tex]a=6*tan(60)[/tex]

[tex]a=6\sqrt{3}[/tex]

Therefore, the correct answer is the letter C.

I hope it helps you!

Answer:

pentagons

Step-by-step explanation:

In fact, there are pentagons which do not tessellate the plane. The house pentagon has two right angles. Because those two angles sum to 180° they can fit along a line, and the other three angles sum to 360° (= 540° - 180°) and fit around a vertex.

Answer:

The Regular Pentagon.

Explanation

I got a 100 % on the quiz

Answer:

The sample mean that will cut off the upper 95% of all samples of size 20 taken from the population is of 1963.2 pounds.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The average breaking strength of a certain brand of steel cable is 2000 pounds, with a standard deviation of 100 pounds.

This means that [tex]\mu = 2000, \sigma = 100[/tex]

A sample of 20 cables is selected and tested.

This means that [tex]n = 20, s = \frac{100}{\sqrt{20}} = 22.361[/tex]

Find the sample mean that will cut off the upper 95% of all samples of size 20 taken from the population.

This is the 100 - 95 = 5th percentile, which is X when Z has a p-value of 0.05, so X when Z = -1.645. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]-1.645 = \frac{X - 2000}{22.361}[/tex]

[tex]X - 2000 = -1.645*22.361[/tex]

[tex]X = 1963.2[/tex]

The sample mean that will cut off the upper 95% of all samples of size 20 taken from the population is of 1963.2 pounds.

Answer:

$9

Step-by-step explanation:

30*(100%-70%)=9

Answer:

9

Step-by-step explanation:

Take the original price

Multiply by the discount percent

30 *70%

30 *.70

21

The discount is 21 percent

Subtract this from the original amount

30-21

9

Answer:

from one point to another, it increases by 1 and right by 2

1/2

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

Pick two points on the line

(0,1) and (2,2)

We can use the slope formula

m = ( y2-y1)/(x2-x1)

   = (2-1)/(2-0)

  = 1/2

Answer:

✔ a strong positive  

✔ strengthen  

✔ increase

ED2021

Answer:

- a strong positive

- strengthen

- increase

Answer:

Step-by-step explanation:

A) Demand per month= 40 cars

Annual Demand (D)= 12*40 = 480

Fixed Cost per order (K)= 15

Holding Cost= 20% of cost= 60 *0.2 = 12

a. Economic Order Quantity=

Q^{*}={\sqrt {{\frac {2DK}{h}}}}

= √(2*480*15)/12

=34.64 ~ 35

Total Cost =P*D+K(D/EOQ)+h(EOQ/2) P= Cost per unit

= 60*480+ 15(480/35) + 12(35/2)

= 28800+ 205.71+ 210

=$29215.71

B). Backorder Cost (b)= $45

Qbo= Q* × √( b+h/ h)

= 35*√(12+45/ 45)

= 35* 1.12

=39.28 ~ 39

Shortage (S)= Qbo * (K/K+b)

= 39* (15/15+45)

= 39* 0.25

= 9.75

Total Cost Minimum=( bS2/ 2Qbo) + P (Qbo- S)2/2Qbo + K(D/Qbo)

=45* 9.752 / 2* 392 + 60 (39-9.75)2/ 2* 392 + 15 ( 480/39)

= 1.40+ 21.9.+ 184.61

=$207.91

C)Length of backorder days (d) = Demand ÷ amount of working days

d = 480 ÷ 300

d = 1.6

Calculate the backorders as the maximum number of backorders divided by the demand per day

s/d = 9.75/1.6 = 6.09 days (answer)

D) Calculate the difference in total between not using backorder:

$207.85 + $207.85 - 207.91 = $207.79

The saving in using backorder is $207.79.

Therefore I would recommend using a backorder

Answer:

Minimum = 8

Maximum = 28

Median = 22

First Quartile = 12

Third Quartile = 26

Step-by-step explanation:

✔️Minimum value = the value at the beginning of the whisker from your left = 8

✔️Maximum value = the value at the end of the whisker to your right = 28

✔️Median = the value at the vertical line that divides the box into two = 22

✔️First Quartile = the value at the beginning of the edge of the box = 12

✔️Third Quartile = the value at end of the edge of the box = 26

9514 1404 393

Answer:

Step-by-step explanation:

In the parallelogram shown, angle B is the supplement of angle DAB:

  ∠B = 180° -77°37' = 102°23'

Angle ACB is the difference of angles 77°37' and 27°8', so is 50°29'.

Now, we know the angles and one side of triangle ABC. We can use the law of sines to solve for the other two sides.

  BC/sin(A) = AB/sin(C)

  AD = BC = AB·sin(A)/sin(C) = (169 lb)sin(27°8')/sin(50°29') ≈ 99.91 lb

 AC = AB·sin(B)/sin(C) = (169 lb)sin(102°23')/sin(50°29') ≈ 213.97 lb

Find the sale price by multiplying the original price by 70% then add the two prices together to get the total.

799 x 0.70 = 559.30

549 x 0.70 = 384.30

Total: 559.30 + 384.30 = $943.60

It’s already in ascending order.

3/5= .6

5/8= .625

5/6= .833

7/4= 1.75

Answer:

Dorcas's Hair Salon

If the customer is not satisfied, the probability that their hair was done by Dorcas is:

=  18.75%

Step-by-step explanation:

Number of hair stylists = 3

                                        Martin        Jennifer       Dorcas     Total

Percentage of haircuts

 done                               27%               30%            43%     100%

Percentage of dissatisfied

 customers                      6%                   7%               3%

Proportion of dissatisfied

 customers                    37.5% (6/16)    43.75% (7/16)   18.75% (3/16)

If the customer is not satisfied, the probability that their hair was done by Dorcas

=  18.75%

9514 1404 393

Answer:

Step-by-step explanation:

The radius is a function of time:

  r(t) = 60t . . . . . radius in cm; time in s

Then the area of the circle is ...

  A = πr² = π(60t)² = 3600πt²

The rate of change of area is the derivative of this:

  A' = 2·3600πt = 7200πt

The rates of change of interest are ...

  after 2s: 45,239 cm²/s

  after 5s: 113,097 cm²/s

  after 6s: 135,717 cm²/s

9514 1404 393

Answer:

  3. sign changes in the denominator need to be taken into account

  4. difference quotient: (f(x+h) -f(x))/h; It is the slope of the secant line. For linear functions, the slope is constant, as is the difference quotient.

Step-by-step explanation:

3. When solving the equation f(x) = 0, where f(x) is a rational function, only the numerator zeros need to be considered.

When solving the inequality f(x) ≤ 0, or f(x) < 0, both numerator and denominator zeros need to be considered. As with solving any inequality, multiplying or dividing by a negative number changes the sense of the comparison.

Example

f(x) = x/(x-2) changes sign at both x=0 and x=2. Then three regions need to be considered when solving f(x) < 0. Those are x < 0, 0 < x < 2, and 2 < x.

__

4. The difference quotient is defined as ...

  dq = (f(x +h) -f(x))/h

The difference quotient is essentially the average slope between (x, f(x)) and (x+h, f(x+h)). That is, it is the slope of the secant line between those two points.

For linear functions, the slope is a constant. The difference quotient is a constant equal to the slope of the line.

Example

f(x) = ax +b . . . . . a linear function with a slope of 'a'

The difference quotient is ...

  (f(x+h) -f(x))/h = ((a(x+h)+b) -(ax+b))/h = (ax+ah+b -ax -b)/h = ah/h = a

The difference quotient is the slope of the line.

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{-12 + (-8) + 30}\\\\\large\textsf{= -12 - 8 + 30}\\\\\large\textsf{-12 - 8 = \bf -20}\\\\\large\textsf{= -20 + 30}\\\\\large\textsf{= \bf 10}\\\\\\\boxed{\boxed{\huge\text{Therefore, your ANSWER is: \textsf{10}}}}\huge\checkmark\\\\\\\\\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

y=-(x+2)(x+4)

y=-(x^2+4x+2x+8)

y=-(x^2+6x+8)

y=-(x^2+4x+2x+8)

Y=-x(x+4)+2(x+4)

y=-(x+2)(X+4)

So vertex is (2,4)

Answer:

[tex]b =6[/tex]

Step-by-step explanation:

Given

[tex]f(x) =3x + b[/tex]

[tex]f(2) = 12[/tex]

Required

Find b

[tex]f(2) = 12[/tex] implies that:

[tex]12 = 3 * 2 + b[/tex]

[tex]12 = 6 + b[/tex]

Collect like terms

[tex]b = 12 - 6[/tex]

[tex]b =6[/tex]

Answer:

15ft

Step-by-step explanation:

By Pythagorean theorem

[tex] {a}^{2} + {b}^{2} = {c}^{2}\\ {a}^{2} + {8}^{2} = {17}^{2} \\ {a}^{2} + 64 = 289 \\ {a}^{2} = 289 - 64 \\ {a}^{2} = 225 \\ \sqrt{ {a}^{2} } = \sqrt{225} \\ a = 15ft \\ [/tex]

Answer:

yes it does

Step-by-step explanation:

because the equation y=9x does not have a y-intercept (all slopes come in the form y=mx+b -- it can be written differently though) and since there is no 'b' that means the y-intercept is 0. So whenever there is no y-intercept, the slope starts at 0.

Option D is correct. 95% of the distribution lies between 1.9975inches and 3.4025inches.

To get the required range of values, we will have to first get the z-score for the two-tailed probability at a 95% confidence interval. According to the normal table, the required range is between -2.81 and 2.81

The formula for calculating the z-score is expressed as;

[tex]z=\frac{x-\overline x}{s}[/tex] where:

[tex]\overline x[/tex] is the mean

s is the standard deviation

z is the z-scores

Given the following

[tex]\overline x[/tex]=2.7 in

s = 0.25

if z = -2.81

[tex]-2.81=\frac{x-2.7}{0.25}\\x-2.7=-2.81*0.25\\x-2.7=-0.7025\\x=-0.7025+2.7\\x=1.9975[/tex]

Similarly:

[tex]2.81=\frac{x_2-2.7}{0.25}\\x_2-2.7=2.81*0.25\\x_2-2.7=0.7025\\x_2=0.7025+2.7\\x_2=3.4025[/tex]

Hence the 95% of the distribution lies between 1.9975inches and 3.4025inches.

Learn more on normal distribution here: https://brainly.com/question/23418254

I think its A) (f+g)(z)=|2x+4|-2

Step-by-step explanation:

Answer:

Here we have the matrix:

[tex]M = \left[\begin{array}{ccc}1&0\\0&3\end{array}\right][/tex]

And we want to find its inverse.

The inverse of a 2x2 matrix A is:

(1/det(A))*adj(A)

where det(A) is the determinant of the matrix.

Such that for a matrix:

[tex]A = \left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right][/tex]

The determinant is:

det(A) = a₁₁*a₂₂ - a₁₂*a₂₁

in the case of our matrix M, the determinant is:

det(M) = 1*3 - 0*0 = 3

and adj(A) is a transposition along the diagonal, and for the other elements, we just change its sign.

Then for our matrix A we would have:

[tex]adj(A) = \left[\begin{array}{ccc}a_{22}&-a_{12}\\-a_{21}&a_{11}\end{array}\right][/tex]

Then for our matrix M, we have:

[tex]adj(M) = \left[\begin{array}{ccc}3&-0\\-0&1\end{array}\right][/tex]

Then the inverse of the matrix M is:

[tex]M^{-1} = \frac{1}{det(M)} *adj(M) = \frac{1}{3}\left[\begin{array}{ccc}3&0\\0&1\end{array}\right] = \left[\begin{array}{ccc}1&0\\0&1/3\end{array}\right][/tex]